HVAC SYSTEMS - HFT Stuttgart

( T −T
) ( T −T
)
col , m
t
amb
col , m
t
Page - 17 -
2
amb
CHAPTER 02
η col = η0
− a1
− a2
(2.2.1-3)
G
G
If the collector mean temperature Tcol,m is approximated by the mean
temperature of the collector inlet Tcol,in and collector outlet Tcol,out
Tcol
, in + Tcol
, out
Tcol
, m = ,
2
(2.2.1-4)
the useful heating power of the collector is given by
( T −T
)
& η &
(2.2.1-5)
Q col = col ⋅G
t ⋅ A = mfluidc
fluid ⋅ col , out col , in
The solution of equation 2.2.1-3 and 2.2.1-5 for the collector outlet temperature
leads to a quadratic equation with the solutions
Tcol , out 1/
2
p
= − ±
2
and the coefficients:
2
⎛ p ⎞
⎜ ⎟
⎝ 2 ⎠
− q
2a1
2m&
fluid ⋅ c fluid
p = + 2T
col , in − 4T
a +
a2
A ⋅ a2
⎛ 2a1
2m&
fluid ⋅ c
q = ⎜ − 4T
a + Tcol
, in −
⎝ a2
A ⋅ a2
⎛G
tη0
a1Ta
2 ⎞
−4
⋅ ⎜ + + T ⎟ a
⎝ a2
a2
⎠
fluid
⎞
⎟ ⋅T
⎠
col , in
(2.2.1-6)
(2.2.1-7)
(2.2.1-8)
This simple model requires only the efficiency parameters of the collector zero
efficiency η0, linear heat loss coefficient a1, and quadratic heat loss coefficient
a2 together with the reference gross aperture or absorber area. These values
are provided on the product datasheet of the collectors. This block was already
available and is called ‘SCETA’ and can be found in the thermal tool box of
INSEL.